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Q.

If α,β are the roots of ax2+bx+c=0 and α+β, α2+β2, α3+β3 are in G.P., where ∆=b2-4ac, then

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a

∆≠0

b

b∆=0

c

cb≠0

d

c∆=0

answer is D.

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Detailed Solution

(α2+β2)=(α+β)(α3+β3)(b2-2aca2)2=(-ba)(-b2+3abca3)⇒4a2c2=acb2⇒ac(b2-4ac)=0As a≠0⇒c∆=0
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If α,β are the roots of ax2+bx+c=0 and α+β, α2+β2, α3+β3 are in G.P., where ∆=b2-4ac, then